Augmented error based adaptive control with improved parametric convergence

This tutorial paper demonstrates, in a systematic way, how the concept of the augmented error, initially proposed for the model reference adaptive control (MRAC), can be used for improvement of parametric convergence. For this purpose, the concept of augmented error is briefly presented, and its properties are analyzed. The basic adaptation algorithms with improved parametric convergence using dynamic regressor extension (DRE) as well as memory regressor extension (MRE) - schemes of Lion and Kreisselmeier - are presented for known and unknown high-frequency gain. Then the augmented error is combined with the techniques of DRE and MRE. As extensions, some ad hoc modifications of the augmented error with DRE and MRE are developed for: MRAC of LTI plants; the adaptive modular backstepping control for some classes of nonlinear plants; adaptive control of plants with input delays. For better clarification, the section with the extensions contains comparable simulation results illustrating the effect of parameteric convergence improvement caused by DRE and MRE. Copyright (C) 2022 The Authors.